There is a map of all the bedrooms you have slept in. You cook in every kitchen. You've traveled to every country you've been to. There is a map of every Universe.
Squeezing this vast trove of detailed information into a small tapestry of neurons is possible thanks to some very clever mathematics.
The patterns of brain cell arrangement that embody the mental representation of physical space could provide insight into times when memory and mapping goes awry.
If you enter a room for the first time, your brain will make a sketch of it. The place cells aren't arranged in a way that mirrors the room, but their coordinated flashing still serves as a way to locate ourselves in a physical area.
As we grow accustomed to the space, the cells are reorganized multiple times into place fields, which in turn creates an enriched network of cells.
From a mathematical point of view, just how this hierarchy develops and operates has been speculative.
The activity of nerve cells in a part of the hippocampus of rats that is critical for their memory of spaces was studied by researchers.
Using a previously devised method for studying place cells in rats as they run mazes, the researchers put a handful of adult rodents through their paces down a straight, 48 meter (157 foot) track.
A sequence of messages passed down through a network can be modeled in a number of ways.
An analysis of the hierarchy of signals flickering across a network of place cells in rats was the best model for our brains to use.
Imagine an office building with a boss sitting alone on the floor. All of the executives below the boss have nice offices. Middle managers are squeezed into smaller suites below them. There are a lot of people on a floor full of cubicles.
The 'linear' hierarchy quickly runs out of room for each individual as you go down the floor.
An office tower constructed using hyperbolic geometry would be able to accommodate new departments on the lower floors if they followed a different set of rules.
While we can use the above example to represent a hyperbolic hierarchy in flat space, those triangles would all be the same size. The outer ends would curve like a floppy hat if this were a piece of material.
Hyperbolic hierarchies use similar mathematics to describe the relationships between different points of activity in a cascade of operations, which allows for a more efficient way to detail distances and objects in our minds.
The researchers observed how small fields of place cells were established when rats were introduced to a new space and how they grew into more complex fields over time.
The brain can act in a variety of ways. Neural networks can be analyzed and understood using hyperbolic geometry and information theory.
Recent studies show that systems in biology follow a hyperbolic hierarchy, which allows animals to categorize smells in a variety of ways.
According to the researchers behind the new study, hyperbolic representations in our spatial awareness adapt better to the reorganization that comes with a growing mental map. If the map was developed according to a linear model, it wouldn't be as accurate.
It is possible to measure similar effects in humans in order to inform models on disease.
The expansion of our mental Universe reflects the expansion of our physical one. There are models that suggest that the total geometry of space-time may have a slight curve.
It's not true that hyperbolic geometry only applies on a Cosmic scale.
Hyperbolic effects are observed on graspable spaces because our brains are slower than light. We would like to learn more about how the brain grows and interacts with one another.
The research was published in a journal.
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